fscchi2
Univariate feature ranking for classification using chi-square tests
Since R2020a
Syntax
Description
ranks features (predictors) using chi-square tests.
The table idx
= fscchi2(Tbl
,ResponseVarName
)Tbl
contains predictor variables and a response variable,
and ResponseVarName
is the name of the response variable in
Tbl
. The function returns idx
, which contains
the indices of predictors ordered by predictor importance, meaning
idx(1)
is the index of the most important predictor. You can use
idx
to select important predictors for classification
problems.
specifies additional options using one or more name-value pair arguments in addition to
any of the input argument combinations in the previous syntaxes. For example, you can
specify prior probabilities and observation weights.idx
= fscchi2(___,Name,Value
)
Examples
Rank Predictors in Matrix
Rank predictors in a numeric matrix and create a bar plot of predictor importance scores.
Load the sample data.
load ionosphere
ionosphere
contains predictor variables (X
) and a response variable (Y
).
Rank the predictors using chi-square tests.
[idx,scores] = fscchi2(X,Y);
The values in scores
are the negative logs of the p-values. If a p-value is smaller than eps(0)
, then the corresponding score value is Inf
. Before creating a bar plot, determine whether scores
includes Inf
values.
find(isinf(scores))
ans = 1x0 empty double row vector
scores
does not include Inf
values. If scores
includes Inf
values, you can replace Inf
by a large numeric number before creating a bar plot for visualization purposes. For details, see Rank Predictors in Table.
Create a bar plot of the predictor importance scores.
bar(scores(idx)) xlabel('Predictor rank') ylabel('Predictor importance score')
Select the top five most important predictors. Find the columns of these predictors in X
.
idx(1:5)
ans = 1×5
5 7 3 8 6
The fifth column of X
is the most important predictor of Y
.
Rank Predictors in Table
Rank predictors in a table and create a bar plot of predictor importance scores.
If your data is in a table and fscchi2
ranks a subset of the variables in the table, then the function indexes the variables using only the subset. Therefore, a good practice is to move the predictors that you do not want to rank to the end of the table. Move the response variable and observation weight vector as well. Then, the indexes of the output arguments are consistent with the indexes of the table.
Load the census1994 data set.
load census1994
The table adultdata
in census1994
contains demographic data from the US Census Bureau to predict whether an individual makes over $50,000 per year. Display the first three rows of the table.
head(adultdata,3)
age workClass fnlwgt education education_num marital_status occupation relationship race sex capital_gain capital_loss hours_per_week native_country salary ___ ________________ __________ _________ _____________ __________________ _________________ _____________ _____ ____ ____________ ____________ ______________ ______________ ______ 39 State-gov 77516 Bachelors 13 Never-married Adm-clerical Not-in-family White Male 2174 0 40 United-States <=50K 50 Self-emp-not-inc 83311 Bachelors 13 Married-civ-spouse Exec-managerial Husband White Male 0 0 13 United-States <=50K 38 Private 2.1565e+05 HS-grad 9 Divorced Handlers-cleaners Not-in-family White Male 0 0 40 United-States <=50K
In the table adultdata
, the third column fnlwgt
is the weight of the samples, and the last column salary
is the response variable. Move fnlwgt
to the left of salary
by using the movevars
function.
adultdata = movevars(adultdata,'fnlwgt','before','salary'); head(adultdata,3)
age workClass education education_num marital_status occupation relationship race sex capital_gain capital_loss hours_per_week native_country fnlwgt salary ___ ________________ _________ _____________ __________________ _________________ _____________ _____ ____ ____________ ____________ ______________ ______________ __________ ______ 39 State-gov Bachelors 13 Never-married Adm-clerical Not-in-family White Male 2174 0 40 United-States 77516 <=50K 50 Self-emp-not-inc Bachelors 13 Married-civ-spouse Exec-managerial Husband White Male 0 0 13 United-States 83311 <=50K 38 Private HS-grad 9 Divorced Handlers-cleaners Not-in-family White Male 0 0 40 United-States 2.1565e+05 <=50K
Rank the predictors in adultdata
. Specify the column salary
as a response variable, and specify the column fnlwgt
as observation weights.
[idx,scores] = fscchi2(adultdata,'salary','Weights','fnlwgt');
The values in scores
are the negative logs of the p-values. If a p-value is smaller than eps(0)
, then the corresponding score value is Inf
. Before creating a bar plot, determine whether scores
includes Inf
values.
idxInf = find(isinf(scores))
idxInf = 1×8
1 3 4 5 6 7 10 12
scores
includes eight Inf
values.
Create a bar plot of predictor importance scores. Use the predictor names for the x-axis tick labels.
figure bar(scores(idx)) xlabel('Predictor rank') ylabel('Predictor importance score') xticklabels(strrep(adultdata.Properties.VariableNames(idx),'_','\_')) xtickangle(45)
The bar
function does not plot any bars for the Inf
values. For the Inf
values, plot bars that have the same length as the largest finite score.
hold on bar(scores(idx(length(idxInf)+1))*ones(length(idxInf),1)) legend('Finite Scores','Inf Scores') hold off
The bar graph displays finite scores and Inf scores using different colors.
Input Arguments
Tbl
— Sample data
table
Sample data, specified as a table. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.
Each row of Tbl
corresponds to one observation, and each column corresponds
to one predictor variable. Optionally, Tbl
can contain additional
columns for a response variable and observation weights.
A response variable can be a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. If the response variable is a character array, then each element of the response variable must correspond to one row of the array.
If
Tbl
contains the response variable, and you want to use all remaining variables inTbl
as predictors, then specify the response variable by usingResponseVarName
. IfTbl
also contains the observation weights, then you can specify the weights by usingWeights
.If
Tbl
contains the response variable, and you want to use only a subset of the remaining variables inTbl
as predictors, then specify the subset of variables by usingformula
.If
Tbl
does not contain the response variable, then specify a response variable by usingY
. The response variable andTbl
must have the same number of rows.
If fscchi2
uses a subset of variables in Tbl
as
predictors, then the function indexes the predictors using only the subset. The values
in the 'CategoricalPredictors'
name-value pair argument and the
output argument idx
do not count the predictors that the function
does not rank.
fscchi2
considers NaN
, ''
(empty character vector), ""
(empty string),
<missing>
, and <undefined>
values
in Tbl
for a response variable to be missing values.
fscchi2
does not use observations with missing values for a
response variable.
Data Types: table
ResponseVarName
— Response variable name
character vector or string scalar containing name of variable in
Tbl
Response variable name, specified as a character vector or string scalar containing the name of a variable in Tbl
.
For example, if a response variable is the column Y
of
Tbl
(Tbl.Y
), then specify
ResponseVarName
as "Y"
.
Data Types: char
| string
formula
— Explanatory model of response variable and subset of predictor variables
character vector | string scalar
Explanatory model of the response variable and a subset of the predictor variables, specified
as a character vector or string scalar in the form "Y ~ x1 + x2 +
x3"
. In this form, Y
represents the response variable, and
x1
, x2
, and x3
represent
the predictor variables.
To specify a subset of variables in Tbl
as predictors, use a formula. If
you specify a formula, then fscchi2
does not rank any variables
in Tbl
that do not appear in formula
.
The variable names in the formula must be both variable names in
Tbl
(Tbl.Properties.VariableNames
) and valid
MATLAB® identifiers. You can verify the variable names in Tbl
by using the isvarname
function. If the variable
names are not valid, then you can convert them by using the matlab.lang.makeValidName
function.
Data Types: char
| string
Y
— Response variable
numeric vector | categorical vector | logical vector | character array | string array | cell array of character vectors
Response variable, specified as a numeric, categorical, or logical vector, a character or
string array, or a cell array of character vectors. Each row of Y
represents the labels of the corresponding row of X
.
fscchi2
considers NaN
, ''
(empty character vector), ""
(empty string),
<missing>
, and <undefined>
values
in Y
to be missing values. fscchi2
does
not use observations with missing values for Y
.
Data Types: single
| double
| categorical
| logical
| char
| string
| cell
X
— Predictor data
numeric matrix
Predictor data, specified as a numeric matrix. Each row of X
corresponds to one observation, and each column corresponds to one predictor variable.
Data Types: single
| double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'NumBins',20,'UseMissing',true
sets the number of bins as 20
and specifies to use missing values in predictors for ranking.
CategoricalPredictors
— List of categorical predictors
vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | "all"
List of categorical predictors, specified as one of the values in this table.
Value | Description |
---|---|
Vector of positive integers |
Each entry in the vector is an index value indicating that the corresponding predictor is
categorical. The index values are between 1 and If |
Logical vector |
A |
Character matrix | Each row of the matrix is the name of a predictor variable. The
names must match the names in Tbl . Pad the
names with extra blanks so each row of the character matrix has the
same length. |
String array or cell array of character vectors | Each element in the array is the name of a predictor variable.
The names must match the names in Tbl . |
"all" | All predictors are categorical. |
By default, if the predictor data is a table
(Tbl
), fscchi2
assumes that a variable is
categorical if it is a logical vector, unordered categorical vector, character array, string
array, or cell array of character vectors. If the predictor data is a matrix
(X
), fscchi2
assumes that all predictors are
continuous. To identify any other predictors as categorical predictors, specify them by using
the CategoricalPredictors
name-value argument.
Example: "CategoricalPredictors","all"
Example: CategoricalPredictors=[1 5 6 8]
Data Types: single
| double
| logical
| char
| string
| cell
ClassNames
— Names of classes to use for ranking
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
Names of the classes to use for ranking, specified as the comma-separated pair consisting of 'ClassNames'
and a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. ClassNames
must have the same data type as Y
or the response variable in Tbl
.
If ClassNames
is a character array, then each element must correspond to
one row of the array.
Use 'ClassNames'
to:
Specify the order of the
Prior
dimensions that corresponds to the class order.Select a subset of classes for ranking. For example, suppose that the set of all distinct class names in
Y
is{'a','b','c'}
. To rank predictors using observations from classes'a'
and'c'
only, specify'ClassNames',{'a','c'}
.
The default value for 'ClassNames'
is the set of all distinct class names in Y
or the response variable in Tbl
. The default 'ClassNames'
value has mathematical ordering if the response variable is ordinal. Otherwise, the default value has alphabetical ordering.
Example: 'ClassNames',{'b','g'}
Data Types: categorical
| char
| string
| logical
| single
| double
| cell
NumBins
— Number of bins for binning continuous predictors
10 (default) | positive integer scalar
Number of bins for binning continuous predictors, specified as the comma-separated pair consisting of 'NumBins'
and a positive integer scalar.
Example: 'NumBins',50
Data Types: single
| double
Prior
— Prior probabilities
'empirical'
(default) | 'uniform'
| vector of scalar values | structure
Prior probabilities for each class, specified as one of the following:
Character vector or string scalar.
Vector (one scalar value for each class). To specify the class order for the corresponding elements of
'Prior'
, set the'ClassNames'
name-value argument.Structure
S
with two fields.S.ClassNames
contains the class names as a variable of the same type as the response variable inY
orTbl
.S.ClassProbs
contains a vector of corresponding probabilities.
fscchi2
normalizes the weights in each class
('Weights'
) to add up to the value of the prior probability of
the respective class.
Example: 'Prior','uniform'
Data Types: char
| string
| single
| double
| struct
UseMissing
— Indicator for whether to use or discard missing values in predictors
false
(default) | true
Indicator for whether to use or discard missing values in predictors, specified as the
comma-separated pair consisting of 'UseMissing'
and either
true
to use or false
to discard missing values
in predictors for ranking.
fscchi2
considers NaN
,
''
(empty character vector), ""
(empty
string), <missing>
, and <undefined>
values to be missing values.
If you specify 'UseMissing',true
, then
fscchi2
uses missing values for ranking. For a categorical
variable, fscchi2
treats missing values as an extra category.
For a continuous variable, fscchi2
places
NaN
values in a separate bin for binning.
If you specify 'UseMissing',false
, then
fscchi2
does not use missing values for ranking. Because
fscchi2
computes importance scores individually for each
predictor, the function does not discard an entire row when values in the row are
partially missing. For each variable, fscchi2
uses all values
that are not missing.
Example: 'UseMissing',true
Data Types: logical
Weights
— Observation weights
ones(size(X,1),1)
(default) | vector of scalar values | name of variable in Tbl
Observation weights, specified as the comma-separated pair consisting of
'Weights'
and a vector of scalar values or the name of a variable
in Tbl
. The function weights the observations in each row of
X
or Tbl
with the corresponding value in
Weights
. The size of Weights
must equal the
number of rows in X
or Tbl
.
If you specify the input data as a table Tbl
, then
Weights
can be the name of a variable in Tbl
that contains a numeric vector. In this case, you must specify
Weights
as a character vector or string scalar. For example, if
the weight vector is the column W
of Tbl
(Tbl.W
), then specify 'Weights,'W'
.
fscchi2
normalizes the weights in each class to add up to the value of the prior probability of the respective class.
Data Types: single
| double
| char
| string
Output Arguments
idx
— Indices of predictors ordered by predictor importance
numeric vector
Indices of predictors in X
or Tbl
ordered by
predictor importance, returned as a 1-by-r numeric vector, where
r is the number of ranked predictors.
If fscchi2
uses a subset of variables in Tbl
as
predictors, then the function indexes the predictors using only the subset. For example,
suppose Tbl
includes 10 columns and you specify the last five
columns of Tbl
as the predictor variables by using
formula
. If idx(3)
is 5
,
then the third most important predictor is the 10th column in Tbl
,
which is the fifth predictor in the subset.
scores
— Predictor scores
numeric vector
Predictor scores, returned as a 1-by-r numeric vector, where r is the number of ranked predictors.
A large score value indicates that the corresponding predictor is important.
For example, suppose Tbl
includes 10 columns and you specify the last
five columns of Tbl
as the predictor variables by using
formula
. Then, score(3)
contains the score
value of the 8th column in Tbl
, which is the third predictor in the
subset.
Algorithms
Univariate Feature Ranking Using Chi-Square Tests
fscchi2
examines whether each predictor variable is independent of a response variable by using individual chi-square tests. A small p-value of the test statistic indicates that the corresponding predictor variable is dependent on the response variable, and, therefore is an important feature.The output
scores
is –log(p). Therefore, a large score value indicates that the corresponding predictor is important. If a p-value is smaller thaneps(0)
, then the output isInf
.fscchi2
examines a continuous variable after binning, or discretizing, the variable. You can specify the number of bins using the'NumBins'
name-value pair argument.
Version History
Introduced in R2020a
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